Mathematics · JEE

Co-ordinate of the centroid, orthocentre and circumcentre of a triangle Mock Test for JEE

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Syllabus context

Part of Co-ordinate Geometry in JEE Main Mathematics.

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Q1MathsUnit 10: Co-ordinate Geometry

P

is any point on the circumcircle of

\triangle A B C

other than the vertices.

H

is the orthocenter of

\triangle A B C, M

is the mid- point of

\boldsymbol{P H}

and

\boldsymbol{D}

is the mid-point of

B C .

Then

Q2MathsUnit 10: Co-ordinate Geometry

If the midpoints of the sides of an equilateral triangle are connected, then they divide it into four triangles all of which are

Q3MathsUnit 10: Co-ordinate Geometry

E

and

F

are the mid-point of sides

B C

CA and

A B

\triangle A B C,

then area

\triangle A B C

area

\triangle \mathrm{DEF}=

Q4MathsUnit 10: Co-ordinate Geometry

In a triangle

A B C,

a line

P Q

is drawn parallel to

B C

, points

P

, Q being on

A B

and

A C

respectively. If

A B=3 A P

then what is the ratio of the area of triangle

A P Q

to the area of triangle

A B C ?

Q5MathsUnit 10: Co-ordinate Geometry

\triangle A B C

is an isosceles triangle with

A B=A C .

Then the line of symmetry for the

\triangle A B C

will be: This question has multiple correct options

Q6MathsUnit 10: Co-ordinate Geometry

If the area of two similar triangles are equal, then they are

Q7MathsUnit 10: Co-ordinate Geometry

The sides of a triangle

A B C

are positive integers. The smallest side has length

l .

What of the following statements is true?

Q8MathsUnit 10: Co-ordinate Geometry

In a

\triangle A B C,

perpendicular

A D

from

A

B C

meets

B C

D .

B D=8 \mathrm{cm}

D C=2 \mathrm{cm}

and

A D=4 \mathrm{cm},

then

Q9MathsUnit 10: Co-ordinate Geometry

An obtuse triangle will have one and only one angle.

Q10MathsUnit 10: Co-ordinate Geometry

In an equilateral triangle

\Delta A B C

with sides

5 \mathrm{cm} .

Angle bisectors of

\angle A, \angle B, \angle C

meet at point

0 .

Measures of OA approximately is

Q11MathsUnit 10: Co-ordinate Geometry

Which condition of congruence will satisfy the diagram?

Q12MathsUnit 10: Co-ordinate Geometry

\mathbf{A}=(-\mathbf{1}, \mathbf{6}, \mathbf{6}), \mathbf{B}=(-\mathbf{4}, \mathbf{9}, \mathbf{6}), \mathbf{G}=

\frac{1}{3}(-5,22,22)

and

G

is the centroid of the

\Delta A B C

then the name of the triangle

\mathbf{A B C}

Q13MathsUnit 10: Co-ordinate Geometry

S

is the circumcentre,

O

is the orthocenter of

\triangle \boldsymbol{A B C}

, then

\boldsymbol{S A}+

\boldsymbol{S B}+\boldsymbol{S C}=

Q14MathsUnit 10: Co-ordinate Geometry

In a triangle

A B C, D

divides BC in the ratio 3: 2 and

E

divides

C A

in the ratio 1: 3. The lines

A D

and

B E

meet at

H

and

C H

meets

A B

F

. Find the ratio in which

F

divides AB.

Q15MathsUnit 10: Co-ordinate Geometry

The position vectors of

\boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D}

are

\bar{a}, \bar{b}, \bar{c}, \bar{d}

respectively and

|\bar{a}-\overline{\boldsymbol{d}}|=

|\bar{b}-\bar{d}|=|\bar{c}-\bar{d}|,

then for the triangle

A B C, D

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